A closely related set of problems is that of one-dimensional water waves that are neutrally stable according to Eq. () but whose amplitudes damp with an algebraic \(t^{-\frac{1}{2}}\)  dependence at long times [1]}, [2]}. Lighthill notes that the damping rate is reduced by a factor of \(t^{-\frac{1}{2}}\)  with the addition of each spatial dimension [2]}.
Herein, we show that this feature is also true of at least two systems that exhibit algebraic growth in 1D.
